Bloomberg sworn in by Giuliani

Former New York Mayor Rudolph Giuliani, left, with his girlfriend Judith Nathan, beside him, swore in Michael Bloomberg just after midnight. Bloomberg's daughter, Emma, stood beside him on the podium.

NEW YORK (CNN) --In his last official act as mayor of New York City, Rudolph Giuliani swore in successor Michael Bloomberg in a Times Square ceremony early Tuesday.

Bloomberg took the oath of office just minutes after the crystal ball slid down the pole in Times Square, marking the start of 2002.

Giuliani left office after two four-year terms as New York's mayor, including a tumultuous final 18 months, including a bout with prostate cancer, a public estrangement with his second wife, and terrorist attacks that brought down the World Trade Center towers.

On Monday morning, Bloomberg took the oath of office at the city clerk's office in lower Manhattan.

After taking the oath, Bloomberg reached into his pocket and gave clerk Victor Robles 15 pennies, the fee for the paperwork.

Bloomberg said the pennies symbolized the "small steps" the city has to take in its recovery from the September 11 attacks.

"We have a long ways to go in this city, but we're going to go a little ways every day," he said.

The clerk gave Bloomberg an apple pin for the city known as the Big Apple.

Talking to reporters, Bloomberg said he expected to be "different" from his predecessors and would not try to emulate their style.

"I'm going to have to work harder than I ever have before in my life," said the billionaire businessman.

He won his first race for public office after spending millions of dollars of his own money. Bloomberg started and ran Bloomberg L.P., a global communications company that provides news and financial services to thousands of businesses worldwide

In addition to the ceremonial swearing-in at midnight New Year's Eve, there will be another one Tuesday at noon.